California lawmakers are pushing this week to pass four bills that would make life easier for immigrants living and working here illegally, but all require the support of a governor who chooses his immigration causes carefully.

Gov. Jerry Brown won praise last fall from Latinos and immigrant communities when he signed a law giving illegal immigrant college students access to state financial aid, but this season he must sift through a more complicated set of measures that opponents view as defying federal prerogatives.

The flurry comes in the last days of the 2012 legislative session and tests the compassion and political future of Brown, who supports a path to citizenship for California’s more than 2 million illegal immigrants but has repeatedly said the solution must come from the federal government.

Already on Brown’s desk is the Trust Act, which would partially pull California out of an immigration dragnet that has deported about 80,000 people from the state since Brown, as attorney general, signed a federal-state partnership in 2009.

“It’s a lottery” whether Brown will sign or veto the Trust Act, said the bill’s author, Assemblyman Tom Ammiano, D-San Francisco. The bill went to the governor’s desk Friday after a 48-26 vote in the Assembly and earlier approval in the state Senate.

Ammiano’s bill would restrict jails from holding immigrants for deportation unless they committed a serious or violent felony. It is meant to counter the Secure Communities fingerprints program that alerts U.S. Immigration and Customs Enforcement whenever local police jail a deportable immigrant.

Immigrant advocates say the federal program deports too many noncriminals and low-level offenders, while most sheriffs support the ICE partnership and want Brown to veto the Trust Act.

Brown and his aides declined to comment on any pending legislation, but he has supported Secure Communities since he was attorney general.

“Every person arrested, their fingerprints are taken and they’re sent to my office, and I now send them to the immigration office,” Brown boasted in a 2010 election debate with his Republican challenger Meg Whitman. “If they’re found to be here illegally, they’re made subject to deportation.”

Ammiano is hoping for a change of heart by Brown and others who the lawmaker says were misled into believing the program was focused on deporting criminals. Brown “signed a boilerplate memorandum of understanding … based on a number of lies, not by him, but by ICE,” Ammiano said.

Also coming soon to Brown’s desk may be a measure by Assemblyman Gil Cedillo, D-Los Angeles, who has until the end of the week to usher through the Legislature a bill that would grant driver’s licenses to young illegal immigrants who get work permits from the Obama administration.

Two other bills were introduced Friday, just one week before the Legislature adjourns for the year on Aug. 31. One surprise proposal known as a “safe harbor” bill seeks to protect most of the state’s undocumented residents by allowing them to work and live in the state if they’ve been here since 2008, have no felony convictions and meet other conditions. Its proponent, Assemblyman Felipe Fuentes, D-Sylmar, introduced the last-minute bill by “gutting and amending” another one focused on vehicle pollution.

The fourth bill, the only one with Republican support, is a mostly symbolic measure to consider work permits for undocumented farm and service workers. Unlike his original version, however, the watered-down bill by Assemblyman Manuel Pérez, D-Coachella, would not actually grant state work permits, but rather would set up a working group to develop the idea.